%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG025-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:26:23 AM UTC 2026
% Result : Unsatisfiable 0.80s 0.57s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 43 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 10 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiply_over_add1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,add(VAR_1,VAR_2)) = add(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',multiply_over_add1) ).
cnf(c_7,plain,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[multiply_over_add1]) ).
fof(multiply_over_add2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(add(VAR_0,VAR_1),VAR_2) = add(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',multiply_over_add2) ).
cnf(c_8,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[multiply_over_add2]) ).
fof(right_alternative,axiom,
! [VAR_0,VAR_1] : multiply(multiply(VAR_0,VAR_1),VAR_1) = multiply(VAR_0,multiply(VAR_1,VAR_1)),
file('theBenchmark.p',right_alternative) ).
cnf(c_9,plain,
multiply(multiply(A,B),B) = multiply(A,multiply(B,B)),
inference(clausify,[status(thm)],[right_alternative]) ).
fof(left_alternative,axiom,
! [VAR_0,VAR_1] : multiply(multiply(VAR_0,VAR_0),VAR_1) = multiply(VAR_0,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',left_alternative) ).
cnf(c_10,plain,
multiply(multiply(A,A),B) = multiply(A,multiply(A,B)),
inference(clausify,[status(thm)],[left_alternative]) ).
fof(commutativity_for_addition,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_for_addition) ).
cnf(c_14,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_for_addition]) ).
fof(associativity_for_addition,axiom,
! [VAR_0,VAR_1,VAR_2] : add(VAR_0,add(VAR_1,VAR_2)) = add(add(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_for_addition) ).
cnf(c_15,plain,
add(A,add(B,C)) = add(add(A,B),C),
inference(clausify,[status(thm)],[associativity_for_addition]) ).
cnf(c_16,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(copy,[status(thm)],[c_15]) ).
fof(right_cancellation_for_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_2
| add(VAR_0,VAR_1) != add(VAR_0,VAR_2) ),
file('theBenchmark.p',right_cancellation_for_addition) ).
cnf(c_18,plain,
( B = C
| add(A,B) != add(A,C) ),
inference(clausify,[status(thm)],[right_cancellation_for_addition]) ).
fof(prove_middle_law,axiom,
multiply(multiply(cy,cx),cy) != multiply(cy,multiply(cx,cy)),
file('theBenchmark.p',prove_middle_law) ).
cnf(c_19,plain,
multiply(multiply(cy,cx),cy) != multiply(cy,multiply(cx,cy)),
inference(clausify,[status(thm)],[prove_middle_law]) ).
cnf(c_369,plain,
multiply(add(multiply(A,add(A,B)),multiply(B,add(A,B))),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_8,c_10]) ).
cnf(c_370,plain,
multiply(add(add(multiply(A,A),multiply(A,B)),multiply(B,add(A,B))),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_7,c_369]) ).
cnf(c_371,plain,
multiply(add(add(multiply(A,A),multiply(A,B)),add(multiply(B,A),multiply(B,B))),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_7,c_370]) ).
cnf(c_372,plain,
multiply(add(multiply(A,A),add(multiply(A,B),add(multiply(B,A),multiply(B,B)))),C) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_16,c_371]) ).
cnf(c_373,plain,
add(multiply(multiply(A,A),C),multiply(add(multiply(A,B),add(multiply(B,A),multiply(B,B))),C)) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_8,c_372]) ).
cnf(c_374,plain,
add(multiply(A,multiply(A,C)),multiply(add(multiply(A,B),add(multiply(B,A),multiply(B,B))),C)) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_10,c_373]) ).
cnf(c_375,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(A,B),C),multiply(add(multiply(B,A),multiply(B,B)),C))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_8,c_374]) ).
cnf(c_376,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(A,B),C),add(multiply(multiply(B,A),C),multiply(multiply(B,B),C)))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_8,c_375]) ).
cnf(c_377,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(A,B),C),add(multiply(multiply(B,A),C),multiply(B,multiply(B,C))))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_10,c_376]) ).
cnf(c_378,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(A,B),C),add(multiply(B,multiply(B,C)),multiply(multiply(B,A),C)))) = multiply(add(A,B),multiply(add(A,B),C)),
inference(paramod,[status(thm)],[c_14,c_377]) ).
cnf(c_379,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(A,B),C),add(multiply(B,multiply(B,C)),multiply(multiply(B,A),C)))) = multiply(add(A,B),add(multiply(A,C),multiply(B,C))),
inference(paramod,[status(thm)],[c_8,c_378]) ).
cnf(c_380,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(A,B),C),add(multiply(B,multiply(B,C)),multiply(multiply(B,A),C)))) = add(multiply(add(A,B),multiply(A,C)),multiply(add(A,B),multiply(B,C))),
inference(paramod,[status(thm)],[c_7,c_379]) ).
cnf(c_381,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(A,B),C),add(multiply(B,multiply(B,C)),multiply(multiply(B,A),C)))) = add(add(multiply(A,multiply(A,C)),multiply(B,multiply(A,C))),multiply(add(A,B),multiply(B,C))),
inference(paramod,[status(thm)],[c_8,c_380]) ).
cnf(c_382,plain,
add(multiply(A,multiply(A,C)),add(multiply(multiply(A,B),C),add(multiply(B,multiply(B,C)),multiply(multiply(B,A),C)))) = add(add(multiply(A,multiply(A,C)),multiply(B,multiply(A,C))),add(multiply(A,multiply(B,C)),multiply(B,multiply(B,C)))),
inference(paramod,[status(thm)],[c_8,c_381]) ).
cnf(c_26,plain,
add(multiply(A,multiply(A,B)),add(multiply(multiply(A,C),B),add(multiply(C,multiply(C,B)),multiply(multiply(C,A),B)))) = add(multiply(A,multiply(A,B)),add(multiply(C,multiply(A,B)),add(multiply(A,multiply(C,B)),multiply(C,multiply(C,B))))),
inference(paramod,[status(thm)],[c_16,c_382]) ).
cnf(c_383,plain,
add(add(A,B),C) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_14,c_16]) ).
cnf(c_31,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(paramod,[status(thm)],[c_16,c_383]) ).
cnf(c_33,plain,
add(multiply(A,multiply(A,B)),add(multiply(C,multiply(C,B)),add(multiply(multiply(A,C),B),multiply(multiply(C,A),B)))) = add(multiply(A,multiply(A,B)),add(multiply(C,multiply(A,B)),add(multiply(A,multiply(C,B)),multiply(C,multiply(C,B))))),
inference(paramod,[status(thm)],[c_31,c_26]) ).
cnf(c_40,plain,
add(A,multiply(multiply(cy,cx),cy)) != add(A,multiply(cy,multiply(cx,cy))),
inference(resolve,[status(thm)],[c_18,c_19]) ).
cnf(c_50,plain,
add(A,add(B,multiply(multiply(cy,cx),cy))) != add(A,add(B,multiply(cy,multiply(cx,cy)))),
inference(resolve,[status(thm)],[c_18,c_40]) ).
cnf(c_384,plain,
add(A,add(B,multiply(multiply(cy,cx),cy))) != add(add(B,multiply(cy,multiply(cx,cy))),A),
inference(paramod,[status(thm)],[c_14,c_50]) ).
cnf(c_385,plain,
add(A,add(B,multiply(multiply(cy,cx),cy))) != add(B,add(multiply(cy,multiply(cx,cy)),A)),
inference(paramod,[status(thm)],[c_16,c_384]) ).
cnf(c_220,plain,
add(A,add(multiply(cy,multiply(cx,cy)),B)) != add(B,add(A,multiply(multiply(cy,cx),cy))),
inference(copy,[status(thm)],[c_385]) ).
cnf(c_386,plain,
add(multiply(A,multiply(A,A)),add(multiply(B,multiply(B,A)),add(multiply(multiply(A,B),A),multiply(B,multiply(A,A))))) = add(multiply(A,multiply(A,A)),add(multiply(B,multiply(A,A)),add(multiply(A,multiply(B,A)),multiply(B,multiply(B,A))))),
inference(paramod,[status(thm)],[c_9,c_33]) ).
cnf(c_241,plain,
add(multiply(A,multiply(A,A)),add(multiply(B,multiply(B,A)),add(multiply(B,multiply(A,A)),multiply(multiply(A,B),A)))) = add(multiply(A,multiply(A,A)),add(multiply(B,multiply(A,A)),add(multiply(A,multiply(B,A)),multiply(B,multiply(B,A))))),
inference(paramod,[status(thm)],[c_14,c_386]) ).
cnf(c_367,plain,
add(A,add(B,add(multiply(cy,multiply(cx,cy)),C))) != add(A,add(C,add(B,multiply(multiply(cy,cx),cy)))),
inference(resolve,[status(thm)],[c_18,c_220]) ).
cnf(c_387,plain,
add(multiply(A,multiply(A,A)),add(multiply(B,multiply(A,A)),add(multiply(A,multiply(B,A)),multiply(B,multiply(B,A))))) = add(multiply(A,multiply(A,A)),add(multiply(B,multiply(B,A)),add(multiply(B,multiply(A,A)),multiply(multiply(A,B),A)))),
inference(copy,[status(thm)],[c_241]) ).
cnf(c_368,plain,
$false,
inference(resolve,[status(thm)],[c_367,c_387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG025-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % Computer : n001.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sat Sep 26 05:52:57 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.37 % Process 1038052 was started by sandbox2 on n001,
% 0.13/0.37 % Sat Sep 26 05:52:57 2026
% 0.13/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.80/0.57
% 0.80/0.57 % SZS status Unsatisfiable for theBenchmark
% 0.80/0.57
% 0.80/0.57 % Proof 1 at 0.15 (+ 0.04) seconds.
% 0.80/0.57 % Length of proof is 18.
% 0.80/0.57 % Level of proof is 5.
% 0.80/0.57 % Maximum clause weight is 47.000.
% 0.80/0.57 % Given clauses 83.
% 0.80/0.57
% 0.80/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------